In terms of equipment you will need at home, we would recommend that you have a short resistance band and a set of dumbbells which can be used in a large number of exercises, as well as having your own exercise mat.
You might also find it useful to purchase additional sets of dumbbells and more short resistance bands of different weights/strengths (so you are able to progressively increase the intensity of your workouts) and one or more long resistance bands.
Should you be interested in purchasing some equipment, please find more information here.